It is already stated in [1]} that for dynamical gravitational structures we have to consider not only the \(\mathbb {C}_{\mathbf {F}}\)  of the system
of the matter configuration, but also the minimal complexity condition of the evolution pattern. To evaluate this condition, it is considered that the systems
evolving in the homologous regime are considered to be the simplest ones (i.e., they correspond to the minimal complexity).
To explain the evolving matter configurations, Herrera et al.[2]} considered a
quasi-homologous condition (\(\mathbb {Q}_{\mathbf {H}}\) ) which is less
restrictive than the homologous condition presumed in
[1]}. The \(\mathbb {Q}_{\mathbf {H}}\) 
condition enables us to examine several physical features of the
dissipative gravitational objects which are significant from
astrophysical perspective.
To formulate the \(\mathbb {Q}_{\mathbf {H}}\)  condition, let us first notice that
Eq.(REF ) can be written as
\(D_{C}\left(\frac{\mathbb {U}}{C}\right) = \frac{\sigma }{C}+\frac{q}{2\mathbb {E}}\left\lbrace 1+(\rho +5P-2P_{r})\eta \right\rbrace -\frac{\varphi _{01}}{2}.\) 
